Archimedes force

Let's do a simple experiment: take a weakly inflated rubber ball and "drown" it in the water. If the depth of immersion is even 1-2 meters, then it is easy to see that its volume will decrease, i.e. From all sides the ball was squeezed by a certain force. It is usually said that hydrostatic pressure is "guilty" here - a physical analog of the force acting in immobile fluids on an immersed body. Hydrostatic forces act on the body from all sides, and their resultant, known as the Archimedian force, is also called the buoyancy force, which corresponds to its direction of action on the body immersed in the liquid.

Archimedes opened his law purely experimentally, and his theoretical justification awaited nearly 2000 years before Pascal discovered the law of hydrostatics for a fixed fluid. According to this law, the pressure is transmitted through the liquid in all directions, regardless of the area to which it acts, on all planes bounding the liquid, and its value P is proportional to the surface S and is directed along its normal. Pascal discovered and tested this law on experience in 1653. According to him, hydrostatic pressure acts on all surfaces from the body immersed in the liquid.

Let us assume that a body in the form of a cube with an edge L to a depth H is immersed in a vessel with water, the distance from the water surface to the upper face. The lower edge is at the depth of H + L. The vector of the force F1 acting on the upper face is directed downwards and F1 = r * g * H * S, where r is the density of the liquid, g is the acceleration due to gravity.

The vector of the force F2 acting on the lower plane is directed upwards, and its value is determined by the expression F2 = r * g * (H + L) * S.

The vectors of forces acting on the side surfaces are mutually balanced, and hence they are excluded from consideration in the future. The Archimedean force is F2> F1 and is directed from the bottom to the top, and is applied to the lower edge of the cube. We define its value F:

F = F2 - F1 = r * g * (H + L) * S - r * g * H * S = r * g * L * S

Note that L * S is the volume of the cube V, and since r * g = p is the weight of a unit of liquid, the Archimedes force formula determines the weight of the volume of the liquid equal to the volume of the cube, i.e. This is just the weight of the fluid displaced by the body. It is interesting to say that the law of Archimedes is possible only for an environment where gravity is present - under zero gravity the law does not work. Finally, the formula of Archimedes' law has the following form:

F = p * V, where p is the specific gravity of the liquid.

Archimedean force can serve as a basis for analyzing the buoyancy of bodies. The condition for the analysis is the ratio of the weight of the immersed body Pm and the weight of the liquid Pg with a volume equal to the volume of the submerged part of the body. If Рт = Рж, then the body floats in the liquid, and if Рт> Рж, then the body sinks. Otherwise, the body emerges until the buoyancy force is equal to the weight of the water pushed out by the drowned part of the body.

Archimedes' law and its use have a long history in technology, starting with the classic example of application in all known crafts and to balloons and airships. The role here was played by the fact that gas refers to a state of matter that completely models the fluid. At the same time, in the air environment, Archimedian force acts on any objects, akin to the same as in a liquid. The first attempts to make an air balloon flight were made by the Montgolfier brothers - they filled the balloon with warm smoke, due to which the weight of the prisoner in the balloon was less than the weight of the same volume of cold air. This was the reason for the appearance of the lifting force, and its magnitude was determined as the difference in weight of these two volumes. Further improvement of the balloons was a burner that continuously heated the air inside the ball. It is clear that the range of flight depended on the duration of the burner. Later, on airships, a gas with a specific gravity lower than that of air was used to fill it.